Superheavy particles of mass $\simeq {10}^{13}–{10}^{14}\hspace{0.5em}\mathrm{GeV}$ with a lifetime $\simeq {10}^{10}–{10}^{22}\hspace{0.5em}\mathrm{yr}$ are very interesting, since their decays may account for the ultrahigh energy (UHE) cosmic rays discovered beyond the Greisen-Zatsepin-Kuzmin cutoff energy $E\sim 5\times {10}^{10}\hspace{0.5em}\mathrm{GeV}.$ We show that the presence of such long-lived superheavy particles is a generic prediction of QCD-like $\mathrm{SU}{(N}_c)$ gauge theories with $N_f$ flavors of quarks and antiquarks and a large number of colors $N_c.$ We construct explicit models based on supersymmetric $\mathrm{SU}{(N}_c)$ gauge theories and show that if the dynamical scale $\Lambda \simeq {10}^{13}–{10}^{14}\hspace{0.5em}\mathrm{GeV}$ and $N_c=6\mathrm{}–10$ the lightest composite baryons have the desired masses and lifetimes to explain the UHE cosmic rays. It is interesting that in these models the gaugino condensation necessarily occurs and hence these models may play the role of the so-called hidden sector for supersymmetry breaking in supergravity.

• Received 2 March 1999

DOI:https://doi.org/10.1103/PhysRevD.60.125009